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中文摘要：
提出一种基于多极边界元法（FM-BEM）的规划-迭代型不完全广义极小残值法（简称IGMRES（m）并建立其收敛性理论．新求解算法采用截断技术，在迭代时仅使用前面计算出的部分向量构造新的递推式计算后面的向量，矩阵和向量的乘积采用多极展开法（FMM）计算，使得计算量和存储量大为减少．通过数试验证明，新算法可有效地处理弹塑性摩擦接触迭代的繁杂和费时问题，在确保数值计算精度的前提下，大大减少迭代次数，显著提高计算效率．
英文摘要：
A new program-iteration pattern algorithm, incomplete generalized minimal residual method （IGMRES（m）） based on the fast multipole boundary element method （FM-BEM）, was proposed for the solution of highly nonlinear equations and its convergence theory was established. With help of truncation technology, a new recursion formulae with the proposed method using only some of the calculated vectors to compute the following vectors, which could greatly reduce the computation and memory requirement. The fast multipole method （FMM） was used to compute the matrix-vector products. Numerical experiments proved that the new algorithm is highly efficient for computing elasto-plastic frictional contact problems, especially for complicated iteration and time-consuming calculation. And it can greatly reduce the iteration times and improve computational efficiency with ensured numerical accuracy.
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